Jeremy Corbyn wins the Labour Party leadership with 251,417 votes. He took to the stage to loud cheers and applause - and hugs party members, including his campaign manager, John McDonnell. Supporters can be heard chanting "Jez we did."

He thanks outgoing leader Ed Miliband and the other candidates and describes the election run-up as "a fascinating experience for all of us."

He applauded everyone who took part in "this huge democratic exercise" which he said has shown Labour to be "passionate, democratic, diverse, united and determined in our quest for a decent and better society".

"We go forward now as a movement and a party bigger than we been for," said the new leader in his final remarks. He said Labour was stronger and more determined than it has been for a long time - and will become more inclusive, involved and democractic, and "shape the future of everyone in this country".

He touched on the refugee and migrant crisis, saying the UK should respond with humanity, support and compassion. "We must recognise that going to war creates a legacy of bitterness and problems.

"Let us be a force for change, humanity and peace in the world. "We are one world," he added.

More support from the international stage as Argentinian President Cristina Fernandez de Kirchner congratulates Jeremy Corbyn, saying he is "a great friend of Latin America and shares, in solidarity, our demands for equality and political sovereignty".

She added: "This is also a triumph for those of us who represent the will to put politics at the service of the people, and the economy at the service of the welfare of all citizens. It is also a triumph for those who advocate for peace and the peaceful resolution of conflicts."

The Hamas-run Al-Risalah website offered support for Jeremy Corbyn's win: "He is one of the most prominent British figures who voiced solidarity with the Palestinian cause and declared his rejection of the war on Gaza."

Jeremy Corbyn's first speech after being elected as new Labour leader was at the 'Refugees Are Welcome' rally to a cheering crowd of thousands at Parliament Square. He hoped that Britain "finds peaceful solutions to the problems of this world".

"We are all humans. We all have a sense of humanity and reaching out to others," he added.

More reaction from Jeremy Corbyn: "Fantastic moment for change in Britain. It's a great day. I was a bit surprised at how big it [the mandate] was. There have been so many magic moments."

He spoke about the support from new members of the Labour Party with those trying to get in to meeting rooms, particularly "young people trying to climb in through the windows - that's how politics has changed."

Jeremy Corbyn thanked his supporters, standing on a chair in a pub after leaving the QEII conference centre. He is heading to the pro-refugee rally in Parliament Square and is expected to speak to crowds at around 4pm.

He will then head to Labour's headquarters before spending the evening at home where he will begin the process of forming his shadow cabinet.

Reaction from Israel: "Far-left MP was long the frontrunner, while some UK Jews expressed alarm over his ties to 'Holocaust deniers, terrorists and some outright anti-Semites'," said the Times of Israel.

Ken Livingstone says Jeremy Corbyn's economic policy can "change the direction of Britain". The new Labour leader's plan for so-called "people's quantitative easing" is the best way to boost investment in the economy, he tells the BBC.

The Bank of England, he adds, had effectively pumped £375bn into the banking system since 2008 but it had "not caused inflation or done harm the economy". He adds: "If you can print money to save the banks, let's print money to modernise Britain."

Michael Fallon, the defence secretary issued the official response to Corbyn's victory on behalf of the Conservative party. "Labour are now a serious risk to our nation's security, our economy's security and your family's security.

"Whether it's weakening our defences, raising taxes on jobs and earnings, racking up more debt and welfare or driving up the cost of living by printing money – Jeremy Corbyn's Labour Party will hurt working people.

"This is a very serious moment for our country – the Conservatives will continue to deliver stability, security and opportunity for working people."

Jeremy Corbyn has apparently left the QEII conference centre by cab on his way to the refugee march in Central London. The march which includes organisations such as Amnesty International, the Syria Solidarity and Stand Up To Racism, is being led by a number of refugees and will end at Parliament Square.

The shadow education secretary Tristram Hunt has said he will not stay in the shadow cabinet under new leader Jeremy Corbyn.

"I will not seek to be part of the front bench. It is important to be honest about it - I have substantial political differences with Jeremy," he told the Press Association:

He added: "We need to congratulate Jeremy on his victory. He has won fair and square and within the rules. He has won handsomely. Now he needs the respect and the space as Labour leader to build his team and go forward."

Labour's shadow energy secretary and unsuccessful deputy Labour leadership contender told the BBC: "I am open to discussions with the new leadership on what role they want me to play to help us win in 2020."

Lord Prescott said it was a "remarkable day" for Labour and says the party has been totally transformed in the past four months. He praised Corbyn's acceptance speech, saying it spoke "to the heart" of Labour members.

He urged those thinking of resigning from the shadow cabinet to think again, saying the party has "overwhelmingly endorsed" Corbyn who he says received more votes than Tony Blair when he won the leadership in 1994.

"The party has spoken with a very strong voice. Get out and fight the Tories," he added.

Sinn Fein president Gerry Adams offers his "warmest congratulations" to the new Labour leader.

"I have known Jeremy for many years. He is a good friend of Ireland and of the Irish peace process. I wish him well in his new and challenging role as leader of the British Labour Party and look forward to working with him in the time ahead to ensure that the gains of the peace process are built upon."

Reactions from the business world: Simon Walker, director general at the Institute of Directors said:

"The IoD congratulates Jeremy Corbyn on his selection as leader of the Labour Party. It is no secret that business has not always seen eye-to-eye with the new leader of the Opposition. From renationalising the railways, to raising taxes on businesses and increasing government spending, Mr Corbyn has proposed some policies in the leadership campaign that we believe would undermine our open and competitive economy. Politicians and business leaders are never in perfect agreement on how the economy should be managed, irrespective of who is in Government, and who in Opposition. We will continue to engage with Labour honestly and directly on behalf our members, who represent businesses large and small across the UK, and hold a variety of political views.

"When Jeremy Corbyn outlined his vision for the future in The Economy in 2020, he said that 'wealth creation is a good thing'. We agree, and hope to work with him on the big economic challenges the UK faces, such as improving the productivity and skills of the workforce. There are important ongoing debates on state investment in infrastructure, how to tackle examples of excessive pay at big companies, and how to increase diversity in senior management. Businesses will make their case sincerely on these issues, and we very much hope the Labour party will be prepared to listen."